The three types of mistake and how to use them in the classroom

When a child makes a mistake in my maths class, my typical response has usually been something along the lines of, “can you spot where you went wrong?” This was useful to a point – we all want to teach children how to learn from mistakes after all. Recently, however, I read something that has made me tweak this slightly.

In The Decision Book, Krogerus and Tschappeler talk about the three different types of mistakes:

real mistakes: these happen when the wrong process is used

black-outs: when part of the process is left out or forgotten

slip-ups: when the right process used, but is carried out incorrectly

Immediately, I could see how this could be useful in maths so I shared the three types of mistakes with my class and we have started trying to identify the type of mistakes that we are making.

Here’s an example of what each could look like when solving the problem below from one of last year’s maths reasoning papers.

Real mistake: start by doing 20 x 140 = 2800cm. This is a real mistake because completely the wrong operation has been used and it should’ve started off with 140 divided by 20 to work out the height of one box.

Black-out: start out correctly by dividing 140 by 20 to get 7 and then take 7 from 140, so the step where 7 had to be multiplied by 3 has been missed out.

Slip-up: again start out correctly, by calculating 140 divided by 20 to get 7. Multiply 7 by 3 to get 21 next and finish with 140 subtract 21, but calculate the answer to this incorrectly and get a final answer of 121cm instead of the correct answer of 119cm.

Identifying the type of mistake is useful because it helps the children (and you) gain more clarity about what they need to work on. If a child made the real mistake above, that tells me they probably don’t actually understand the problem here at all or what they’re trying to find out. My next step would probably be to find out if they can explain what they need to find out in words before we go into calculations. They may well just be grappling at numbers and doing something – anything! – with them to get an answer. This is a bigger problem to unpick than a child who has made the slip-up mistake. This could just be down to not double checking their work or rushing. However, I would be able to clearly see they do understand the context of the problem and can identify what operations and methods they need to use. If a child had made the black-out error, I’d know they understood the context of the problem, but weren’t focussing on the final answer and needed to work on the second or third step of multi-step problems.

This is something I’m going to continue to explore and use to help children reflect in maths and possibly beyond. It’s a simple switch from asking “can you spot where you’ve gone wrong?” to “can you spot how you’ve gone wrong?” and focussing on that when we’re unpicking mistakes together.